含噪声高维数据的稀疏主成分分析的极小极大界
MINIMAX BOUNDS FOR SPARSE PCA WITH NOISY HIGH-DIMENSIONAL DATA.
作者信息
Birnbaum Aharon, Johnstone Iain M, Nadler Boaz, Paul Debashis
机构信息
School of Computer Science and Engineering Hebrew University of Jerusalem The Edmond J. Safra Campus Jerusalem, 91904 Israel
Department of Statistics Stanford University Stanford, California 94305 USA
出版信息
Ann Stat. 2013 Jun;41(3):1055-1084. doi: 10.1214/12-AOS1014.
We study the problem of estimating the leading eigenvectors of a high-dimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the risk points to the existence of different regimes of sparsity of the eigenvectors. We also propose a new method for estimating the eigenvectors by a two-stage coordinate selection scheme.
我们研究基于独立高斯观测值估计高维总体协方差矩阵的主特征向量的问题。在总体特征向量的各种稀疏模型下，当维度和样本量联合趋于无穷时，我们建立了估计量在该损失下的极小极大风险的下界。风险的下界表明特征向量存在不同的稀疏模式。我们还提出了一种通过两阶段坐标选择方案来估计特征向量的新方法。
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